2. F = ma. Newton s Laws. 1. Bodies stay at constant velocity unless acted on by outside force!

Transcription

1 Newton s Laws review 1. Bodies stay at constant velocity unless acted on by outside force! Defines mass, m, as 2. F ma all that act on the body parameter reflecting body s resistance to motion 3. Action Reaction! When force acts on body 2 by body 1, then equal and opposite force acts on body 1 by body 2. slide 1

2 Forces on the isolated pieces (sometimes called free body diagrams) N f f 1 2 kxjˆ N Fceiling f + f 1 2 No acceleration Forces on all bodies balance kxjˆ slide 2

3 Sample Prob 5-6: Rope tensions? Rigid ceiling Illustrates force problem procedures 1. Draw Picture and analyze the problem 2. Isolate specific points or bodies and sketch forces acting on these 3. Use SFma at each point If a0, net force at the point is zero slide 3

4 Problem 5-34 The figure shows four penguins that are being playfully pulled along very slippery (frictionless) ice by a curator. The masses of three penguins and the tension in two of the cords are given. Find the penguin mass that is not given. slide 4

5 Sample Prob 5-8 a The weight recorded on the scale is N! Not F g! If a 0, then N F g mg. But if a is not zero, more complicated use Newton! (Note that scale feels a force equal to N.) Reading kx N F ma g N mg ( + a) inside the scale Nkx N Scale can read anything from 0 to Note if a -g, must rethink! slide 5

6 Sample Prob 5-7 N mg cosθ T mg sinθ slide 6

7 Sample Prob 5-7 with string cut N mgcosθ since a 0 y mgsinθ ma so a g x sinθ slide 7 x intuitive answer?

8 + N One Step Harder Problem T T + no friction T mgsinθ ma 1 1 q m 1 g m 2 g mg T ma 2 2 mg ( mgsin θ + ma) ma mg mgsin θ ( m + m ) a a g m m 2 1 m sinθ m Check get intuitive answers in limiting cases slide 8

9 Accelerometer Measure the acceleration of the car by measuring the angle of the string! Try it in the subway! F F a T T sinθ ma cosθ mg g tanθ slide 9

10 Problem 5 43 (not assigned) 10 kg monkey (m) 15 kg package (M) no tree friction How can monkey raise the pckage? Monkey pulls on rope with force T T (uniform tension throughout rope) Net force on monkey T Net force on package Find minimum acceleration of monkey in order to lift package! mg T Keep in mind when you do problem 5-50 Mg slide 10

11 Friction Approx f max s µ s N f k µ k N slide 11

12 Details of friction static kinetic The tablecloth trick slide 12

13 Problem: Raise the book until coin starts to fall Measure the angle Calculate the coefficient of static friction f s N Example of finding coefficient of friction mg mg sinθ cosθ fs µ s tanθ N slide 13

14 Fluid Drag Forces Nonviscous flow (only thing considered ch 15) no drag force Viscous but laminar Viscous and turbulent Fd Fd D Kv D 1 2 C rav 2 slide 14

15 Drag Considered Ch 6 Turbulent Cat falls and accelerates until D F g At that point, cat has reached terminal velocity See specific discussion in section 6-3. D drag force, oppose motion D 1 2 C rav 2 slide 15

16 Terminal Speed In between: dv m mg Kv η dt D m v v (1 e ) In either case, D - v 1 or 2 Object will attain a terminal speed Text does the turbulent flow case Laminar flow case: Kv η D mg when v v with solution for start at rest term Kη t [culture] term mg Kη slide 16

17 HW Problem 6-45 (assigned) r LIFT v v 2 Airplane in holding pattern flying in circle of radius, r, at constant speed, v a r Given v and bank angle, what is r? WEIGHT slide 17

18 Centripetal Force centripetal force.mov Must always be a force to hold an object in circular motion This force supplies the centripetal acceleration! Hey! What happened to centifugal force? T 2 v m R slide 18

19 Centrifugal Force is a FICTION! Real life experiences that make clear objects without force travel in a straight line at the velocity with which they started! slide 19

20 Conclusion HW 2 due on Monday (problems ch 4,5,6) Read Chapter 7 before Monday lecture Sample Midterm 1 at website on Monday Will include the solutions Recommend strongly you try it before reading solutions Midterm exam in class following Monday 9/29 Will cover chapters 1 6 slide 20